Horizontal Electric Currents Research Articles

Competition of localized thermal buoyancy and Lorentz forces in an electrolyte enclosed in a cavity

We study the flow of an electrolyte inside a slender square cavity produced by two competing localized forces, the thermal buoyancy force produced by the heating of a central part of the horizontal bottom wall and a vertical downward Lorentz force. This force is produced by a constant horizontal electric current between the slender vertical walls and a couple of circular magnets with opposing polarization placed on the center of both square vertical walls. The flow inside the cavity is considered two dimensional and simulated using the lattice Boltzmann equation method. We find the map of the flow patterns and their transitions for a Grashof number Gr in the range 0≤Gr≤4×103 and a Chandrasekhar number Ch in 0≤Ch≤1×107. For Gr≤2×103, the plane Gr-Ch can be divided in three regions with sharp changes in the flow patterns and the average Nusselt number on the top wall and the average asymmetry. One region is dominated by the buoyancy force, another by the Lorentz force, and there is an intermediate one, where neither of these forces dominates. For larger Gr, there are no sharp transitions.

The onset of instabilities and finite amplitude waves in a model of aluminum reduction cells with nonuniform cathode current

In aluminum reduction cells, the electric current density at the cathode is seldom uniform. This may be due to a variety of reasons. One of the reasons is that a mass of undissolved alumina may get enrobed by the cryolitic bath, and this mix freezes due to the decrease in temperature below the liquidus point. Thus, an electrically resistive solid layer (“mud”) is formed at a part of the cathode. This leads to horizontal electric currents in the liquid aluminum layer, and their magnetohydrodynamic (MHD) interaction with the vertical magnetic field induces a rotating flow of aluminum. This may cause undesirable MHD instabilities. A quasi-two-dimensional model for the laboratory facility has been presented. The results show that the dominating feature of the flow is a depression of the free surface of the liquid metal above the mud spot. This is due to strong rotation of the liquid metal around the mud spot, which causes the centrifugal force. Other effects may include superimposed conventional MHD instability, which manifests itself in a rotating interface, modulated waves, reflection of the waves from the corners of the domain, sloshing, etc. It has been shown that small mud spots do not affect the cell stability, while the large ones may cause such deep depressions that the centrifugal force completely removes the liquid metal above the spot.

Design of segmented off-diagonal thermoelectric generators using topology optimization

A density-based topology optimization methodology is used to optimize the off-diagonal figure-of-merit and off-diagonal electrical power output of thermoelectric generators by distributing two different thermoelectric active materials in a two dimensional design space. Off-diagonal thermoelectric generators are characterized by converting a vertical thermal heat flux into a horizontal electric current, and may be useful in applications where the electrodes connected to the generator are prone to thermo-mechanical stress and wear.With basis in the topology optimization framework and a sequence of numerical examples, we discuss critical and important model parameters such as objective functions, heat transfer rates and device lengths. All results are supported by exhaustive crosschecks and validations, and it is shown that the off-diagonal figure-of-merit and the off-diagonal electrical power output may be improved by 233% and 229%, respectively, compared to other optimization approaches available in the literature.

Influence of an electromagnetic field on the formation of wet metal foam

This paper presents a method of floating bubbles in liquid metal by applying an electromagnetic field. The aim of this method is to distribute the bubbles more homogeneously and to stop drainage in the generation process of metal foam. A horizontal electric current, combined with an orthogonal, horizontal magnetic field creates an upward Lorentz force that counteracts gravitational acceleration. Phase-resolving numerical simulations have been applied in order to investigate the complex behavior of a large number of bubbles exposed to these fields. Controlled by the strength of the electromagnetic fields, the bubbles can ascend more slowly, stagnate, or even descend. Due to the influence of the bubbles on the electric current, however, rotating flows are induced which prevent the bubbles from becoming immobile and induce an interesting mixing structure. Consequently, the applied electromagnetic field offers the opportunity to manipulate the bubble distribution and the drainage in the generation process of wet metal foam.

Remote reservoir resistivity mapping

A method for surface estimation of reservoir properties, wherein location of and average earth resistivities above, below, and horizontally adjacent to the subsurface geologic formation are first determined using geological and geophysical data in the vicinity of the subsurface geologic formation. Then dimensions and probing frequency for an electromagnetic source are determined to substantially maximize transmitted vertical and horizontal electric currents at the subsurface geologic formation, using the location and the average earth resistivities. Next, the electromagnetic source is activated at or near surface, approximately centered above the subsurface geologic formation and a plurality of components of electromagnetic response is measured with a receiver array. Geometrical and electrical parameter constraints are determined, using the geological and geophysical data. Finally, the electromagnetic response is processed using the geometrical and electrical parameter constraints to produce inverted vertical and horizontal resistivity depth images. Optionally, the inverted resistivity depth images may be combined with the geological and geophysical data to estimate the reservoir fluid and shaliness properties.

Study of small-amplitude magnetohydrodynamic surface waves on liquid metal

Magnetohydrodynamic (MHD) surface waves on liquid metal are studied theoretically and experimentally in the small magnetic Reynolds number limit. A linear dispersion relation is derived when a horizontal magnetic field and a horizontal electric current is imposed. Waves always damp in the deep liquid limit with a magnetic field parallel to the propagation direction. When the magnetic field is weak, waves are weakly damped and the real part of the dispersion is unaffected, while in the opposite limit waves are strongly damped with shortened wavelengths. In a table-top experiment, planar MHD surface waves on liquid gallium are studied in detail in the regime of weak magnetic field and deep liquid. A noninvasive diagnostic accurately measures surface waves at multiple locations by reflecting an array of lasers off the surface onto a screen, which is recorded by an intensified-CCD (charge-coupled device) camera. The measured dispersion relation is consistent with the linear theory with a reduced surface tension likely due to surface oxidation. In excellent agreement with linear theory, it is observed that surface waves are damped only when a horizontal magnetic field is imposed parallel to the propagation direction. No damping is observed under a perpendicular magnetic field. The existence of strong wave damping even without magnetic field suggests the importance of the surface oxide layer. Implications to the liquid metal wall concept in fusion reactors, especially on the wave damping and a Rayleigh–Taylor instability when the Lorentz force is used to support liquid metal layer against gravity, are discussed.

Estimating horizontal electric current in solar active regions

Within the framework of nonlinear force-free field models, we have developed a relaxation scheme for estimating horizontal electric currents in solar active regions. The test case which uses an analytical solution shows that at each iteration step the average Lorentz force decreases rapidly and the values of partial derivative B-x/partial derivative z and partial derivative By/partial derivative z converge well toward analytical ones. As a result the computed horizontal electric currents and analytical ones show good agreement in both distribution and magnitude. This scheme has avoided mathematical singularities along the inversion line B-z = 0 which appeared in the previous extrapolating methods. Then this newly developed scheme is used to analyze the vector magnetogram of a Rare-prolific region NOAA 6659. The computational results show the following: (1) The distribution of horizontal electric current and vertical electric current share a similar configuration. (2) Near the separator of a quadrupole field configuration of this active region there is a confined region of strong horizontal electric currents, near which a white-light flare took place on the same day.

Prediction of the interplanetary magnetic field strength

A new model of the coronal and interplanetary magnetic field can predict both the interplanetary magnetic field strength and its polarity from measurements of the photospheric magnetic field. The model includes the effects of the large‐scale horizontal electric currents flowing in the inner corona, of the warped heliospheric current sheet in the upper corona, and of volume currents flowing in the region where the solar wind plasma totally controls the magnetic field. The model matches the MHD solution for a simple dipole test case better than earlier source surface and current sheet models. The strength and polarity of the radial interplanetary magnetic field component predicted for quiet time samples in each year from 1977 to 1986 agree with observations made near the Earth's orbit better than the hybrid MHD‐source surface model (Wang and Sheeley, 1988). The results raise the question of whether coronal holes are the only solar source of the interplanetary magnetic field in the solar wind. If some interplanetary flux originates outside coronal holes, the model can match the observed field using the accepted 1.8 saturation correction factor for λ5250 Å magnetograph observations. Requiring open flux to come exclusively from coronal holes requires an additional factor of two.

Electromagnetic Mode Conversion By Surface-Conductivity Anomalies: Applications For Conductivity Soundings

SUMMARY A natural-source electromagnetic sounding of the earth made near a surface conductivity anomaly will resolve different features of the underlying conductivity structure than a sounding in a more uniform region. the surface-conductivity anomaly deflects horizontal electric currents induced by an external source into a vertical plane converting transverse-electric (TE) mode currents into the transverse (TM) mode. the resulting current distribution involves both vertical current flow and spatial variations with shorter wavelengths than the external field, providing increased resolution of resistive layers and of the conductivity structure at shallow depths. We exmine the sensitivity of the converted-mode response for the vertical-gradient sounding (VGS) method in order to plan electromagnetic soundings in a narrow ocean strait such as the Strait of Georgia between Vancouver Island and the Canadian mainland. An integral-equation method is used to model the current system induced by a mode converter, consisting of a known conductivity structure, such as a body of ocean water. It is shown that the depth of penetration of the secondary current distribution produced by the mode converter depends on both the horizontal scale of the feature and the distance from its edge. Within this depth range the current system is strongly perturbed by the existence of either conductive or resistive layers. the sensitivity of the VGS response (the ratio of the horizontal magnetic field at the base and surface of the mode converter) is examined using forward modelling of layered conductivity structures. the response is found to be dependent on both the TE and TM current systems. For a narrow ocean strait such as the Strait of Georgia, a measurement of the converted-mode VGS response along a line of sites on the floor of the strait, will provide resolution of conductive and resistive layers in the upper 10 km. the appropriate frequency range over which the VGS response should be measured in the strait is 10−2 Hz to 10 Hz. In our investigation of mode conversion we examine both the frequency- and time-domain response. Snap shots showing the current system evolving in the earth after a step or impulse illustrate the interaction of the EM signals with resistive and conductive layers. We show that the time-domain response can be used in a ‘geometrical sounding’analogous to seismic refraction to determine the conductivity structure. Finally we examine the limitations on the accuracy of the frequency and time-domain VGS response imposed by natural signal levels and instrument sensitivity.

Areal coverage of spurious reversals of the earth's magnetic field.

The Laschamp event ended between 8000 and 20000 years ago. In several other parts of the world, excursions of the Earth's magnetic field have been seen at about this time interval, but at other parts, notably in the Aegean sea, there is no evidence for a reversal or excursion of the field during this time. By using a two dipole model, we have shown that it is possible to produce an apparent reversal at one point on the Earth's surface, which produces deviations in the direction of the magnetic field over a rather small area around the position of reversal. The two dipoles used were a centered axial dipole to model the main magnetic field, and a dipole located at the top of the core, to produce the reversed field above it. Our models show that the data from the Aegean sea are not contradictory with the Laschamp event provided that it is a pseudo reversal. We have also shown that if the non-dipole field is caused by horizontal electric currents at the top of the core, then pseudo reversals are more likely to occur at high latitudes than at low latitudes.

Motionally induced electric and magnetic fields in the sea

Motionally induced electric and magnetic fields are investigated in the sea, crust, and mantle for large-scale low-frequency oceanic flows. It is shown that three-dimensional flows generate large-scale horizontal electric currents not present in two-dimensional motions. The resulting induced magnetic fields penetrate into the mantle inducing there electric currents. The degree of mutual induction between the ocean and the mantle depends on the parameter δmL, the ratio of the electromagnetic skin depth of the mantle to the horizontal scale of the flow. For δmL≫1 there is little mutual induction whereas for δmL≪1 there is strong coupling between the ocean and the mantle. It is shown that the variable *, the conductivity-weighted, vertically averaged velocity is important in the generation of both local and large-scale electric currents. Expressions are derived showing that , the vertically averaged velocity, can be determined from measurements of the induced electric and magnetic fields at the sea floor. Several special cases are calculated illustrating the influences of the mantle, the conducting sediments, and the horizontal scales of the motion.

Effects of the auroral electrojet on the scattering and absorption of fast electrons in the upper atmosphere

A single-scattering Monte Carlo technique is used in studying the effects horizontal electric currents in the ionosphere exert on the scattering and absorption of precipitated electrons of energies > 1 keV. The computer programme developed for this task allows arbitrary energy and angular distributions to be employed. It is found that in the vicinity of the current, appreciable distortion in the local electron density occurs. The electrojet also causes anomalies in the electron albedo, and increases as well as decreases may occur.

地球磁氣の原因としての水平電流に就いて(第二報)

In the first paper, the present author has attacked the same problem using the data given in A. Schmidt's paper, but some important points were remained untouched there. These point are such as those of the assumption of the variation of the magnetic force with height, the error accompanied by the calculation and the recalculation based on the new and precise data of the magnetic force. In this paper these important problems are discussed with an additional notice on the physical interpretation of the current.(a) In the first paper, the present author adopted the following expression after the wireless research made by Appleton and Builder:This expression is the same as that which shows the distribution of the magnetic force near the earth's surface when a magnet was placed at the centre of the earth. Then the values of the magnetic force on the earth's surface calculated by the above assumption are considerably different from the observed ones. The expression which characterizes, without serious error, the distribution of the magnetic force on the earth's surface was already given by Gauss and others. This expression may afford us a criterion of the expression used in the first paper.According to Gauss, the components of the magnetic force are expressed byIf we put r=R+h, we haveThe observation shows us that the second term of the right hand side of this expression is of the order of 1/10 or so as compared with the first term. This means thatThe expression (1) is able to be used if h/R is of the order of 1/10, namely if we consider h to be of the order of several hundred kilometers.Therefore the horizontal electric current calculated in the first paper is the average current in the region extending from the earth's surface to the upper atmosphere of several hundred kilometers of height, generally including the ionosphere.(b) The values of the magnetic force adopted in the first paper were based on those given in A. Schmidt's paper. Therefore the original value may have a considerable error of 100γ or so. Thus the average value _??_0 or _??_0 obtained by the graphical method will be accompanied by the error of 500γ or so. Thus the expressions 2α_??_0+Z0A-Z0B and 2 sin θβ_??_0+Z0A'-Z0B', each of them is of the order of 1, 000γ, will have, the error less than 500γ. Thereforethe calculated value of the horizontal electric current may generally lie out of the error.(c) The above discussions show us that the treatment in the first paper is not meaningless. Hence the author recalculated the horizontal current according to the data given by the magnetic surveying in 1922.In this paper the average values as to the latitude were calculated with the following result.The horizontal electric currents flow generally to the direction of the east and west as is tabulated in Table 1 and schematically given in Fig. 2. (pp. 61, 62.)The comparison of the current calculated from the data given in A. Schmidt's paper with those obtained in 1922 is graphed in Fig. 1, showing that the average features of the current are very similar.(d) It is concluded that the current is directed to east in the northern part than 30°N and in the region between the equator and 50°S. In the other part of the earth the current flows westwardly. The intensity of the current is of the order of 1amp/km2 and it is somewhat great at the polar caps.As in the upper atmosphere there exist the ionosphere with considerably deep distribution, the current of the same order of the above calculated value will be flowing in the ionosphere.